Mr Bodley was a composer of vocal, chamber and orchestral music, as well as five symphonies, and was a founding member of Áosdána, an association comprised of some of the country’s top artists.
The Arts Council has expressed its “great sadness” at the passing of Mr Bodley, who died on Friday at the age of 90.
He was the first composer to be awarded the honour of ‘Saoi’ by the members of Aosdána, conferred on him by President Mary McAleese in 2008.
Also paying tribute President Michael D Higgins said the contribution of Seóirse to music composition was of immense significance and as a teacher he will be greatly missed.
“I have no doubt whatever that his unique legacy will endure for generations to come. There are so many who recall his time as Professor of Music at University College Dublin for over four decades.
“That this was recognised by the conferring of an Honorary Doctorate on Seóirse by the National University of Ireland just a few weeks ago was warmly welcomed and so well earned,” he said.
President Higgins said he recalls the warmth of his personality and the great affection, as well as respect, in which he was held by students and colleagues.
“Sabina joins me in sending our deepest condolences to his beloved and devoted wife, Professor Lorraine Byrne Bodley, and to his family and many friends and colleagues at this time of great loss.
“I hope that many happy memories, as well as the endurance of Seóirse’s exceptional legacy, will serve as a consolation now. It is one that will never be forgotten,” he added.
Meanwhile, the Arts Council said his long career, adopting many styles, always reflected his profound sense of being “both Irish and international, modern and conscious of his musical heritage.”
Professor Kevin Rafter, Chair of the Arts Council said he remembers Mr Bodley as one of the most important figures in Irish composition of the latter part of the 20th century.
He said the celebrity composer held a great outward-looking internationalism as well as a deeply personal engagement with his Irish musical heritage.
This helped Mr Bodley in forging what was “always a uniquely true expression” of himself and his time and place, Prof Rafter said.
“He was greatly liked and admired by his many composition students in UCD, his colleagues in Aosdána and a wide circle of friends.
“On behalf of the Arts Council, I would like to express our sincere sympathy to his wife Lorraine and the Bodley family for their great loss,” he added.
Mr Bodley saw his work performed extensively during his lifetime, not just in Ireland, but throughout Europe and as far afield as China, North America, Japan and Australia.
The Arts Council described him as “the most internationally pre-eminent Irish composer of his generation.”